Logic

Quotations

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This blog very frequently includes quotations. Some posts are essentially nothing but a quotation, as this one here, and others do not contain much beyond a series of long quotations, as for example this one.

Why do I use the thoughts of others rather than putting things in my own words? There are a number of reasons. It is very practical. It is much easier to compose a long blog post using quotations, while it takes a lot of time and energy to write everything yourself. And the idea of originality here is not really relevant. For as Qoheleth says, “What has been is what will be, and what has been done is what will be done; there is nothing new under the sun.” Most of the positions argued on this blog have been argued by others, and there is nothing surprising about this. In addition, insofar as a new contribution is possible, one can do this by organizing the thoughts of others, just as Socrates teaches the boy by helping him organize his thoughts. 

But the most important reason is the following. Speakers and writers are addressing people, and just as beliefs have motives, so the act of speaking or writing has a motive. And whether or not people approve of doing this, the listener or the reader tends to think of these motives. As Alexander Pruss discusses in a blog post here, sometimes such considerations are necessary. Nonetheless, this can lead people away from understanding reality. If instead of thinking about what I am saying and what is true about it, someone thinks, “Why is he saying this?”, this can hinder them in their understanding of the truth of the matter.

Quotations are very helpful in reducing this effect. Since a quotation is taken out of context, it is removed from the motivation of the original speaker. Yes, there is still a motive on the part of the person who includes the quotation. But the reader who reads the quotation knows that it is not addressed to him in the manner of the original. He does not need to say, “Why is the original author saying this?”, because it does not matter in the new context. The only thing that matters is what he is saying, not why he is saying it. So it provides some impetus towards considering the truth of the matter. This remains true whether the quotation itself says something which is true, or something which is false.

I Respond

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If we consider the last two posts, we can see that they resemble a disputed question. However, unlike St. Thomas’s Summa Theologiae, and instead in the technical manner of a disputed question, there are arguments on both sides. Additionally, I did not include the typical “response of the master,” nor did I include responses to the arguments. I will explain these omissions shortly.

James Chastek, in the passage quoted here, asserted that it is difficult to make your opponent’s arguments without relating to them as something to be refuted. As we have seen from these examples, there is actually no big difficulty here, and historically this was done with the disputed question. In principle people could even write books this way, and they probably have, on occasion. One could write an entire book on the actual infinite with the structure, “Part I: An Actual Infinite is Possible,” and “Part 2: An Actual Infinite is Impossible.”

There are a lot of reasons why people don’t do this in general, and why for example I would not write blog posts like this in general. One factor is the practical issue that it is twice as much work. Another is the concrete goal of a book or a blog post.

Why did I not include the response of the master? In the medieval schools, the arguments on each side were formulated by the students, followed by the master’s response and his answers to the arguments. Thus, since the master did not compose the original arguments, he could make a new argument for his conclusion, outside of the original arguments. But since I was the one composing the arguments on each side, if I thought there was a very strong argument for one conclusion, I could simply include it there. Consequently a special response would simply repeat something contained in the series of arguments.

But there is more to it than this. A special response would also give away my personal opinion, which I preferred to avoid. If I could simply state the strong arguments in the series, nothing would be added by restating it as the “response of the master” except the bare fact that I agree with the one side rather than the other.

Consider how students will react to such a thing in real life. In terms of the argument, nothing is added to their understanding of reality by this response. Nonetheless, they receive additional evidence in favor of one conclusion, namely that the teacher agrees with one side. So they will have an additional reason to agree with that side, a real reason, but not one that adds to their understanding of the issues. Thus, to the degree that they believe that this response has contributed to their understanding, they are simply mistaken, and consequently believe that they understand things better than they do.

The issue of the responses to the arguments in somewhat different. If someone wrote the above book on the Actual Infinite, presumably Part I would also include responses to the main arguments in Part II, and Part II would include responses to the main arguments in Part I. This is in fact very important for understanding. Although arguments are never one-sided, they are frequently mostly one-sided, where most of the best arguments and evidence are indeed on one side. And in such cases, this usually becomes most clear when one considers the responses to the opposing arguments, and, consequently, where one begins to actually understand the matter at hand, and to recognize the truth of the matter.

So I did not include such responses because most likely they would reveal more clearly which side had the stronger argument, and which side I agreed with. But note that in principle these two things would be the same: the reasons which would show that I agreed with one side, would show that this was the better and more likely side. In practice of course there might be other ways that someone could guess my opinion, as for example from the style of the arguments and so on. (For the record, my opinion cannot be determined by which side went first; that was determined by the flip of a coin.)

Someone once posted on Twitter (I can no longer find the particular post) something along the lines of, “How can you be unbiased if I can tell which side you are on?” We can see here that in fact there is a valid answer to this: if I simply present all of the best arguments for both sides, together with their responses, then you can tell which side I am on by determining which side is probably right, and the fact that you can determine my side in that way does not suggest that I am biased. On the other hand, if you note that I have missed strong and important arguments on the side of the part that seems weaker in my presentation, that might be a reason for thinking that I am biased.

That said, the responses to the arguments in the previous posts, and consequently the “response of the master,” is left here as an exercise for the reader.

Making Your Point vs. Understanding Reality

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Generally speaking, people who write something know in advance what they are going to say, and not surprisingly, they agree with it. Along these lines, Hal Finney says in this comment:

Michael Ruse is quoted above as saying, “The God Delusion makes me embarrassed to be an atheist, and the McGraths show why.” That’s very much to his credit, that although he agrees with the conclusion of Dawkins’ book, he disagrees with the arguments. You don’t often get people willing to make these kinds of public statements that undercut arguments in favor of their beliefs.

Sounds like McGrath himself is a theist, unfortunately, so his book is arguing for a conclusion he believes in, as did Dawkins. And of course, as is true for virtually 100% of books every published. Can you imagine a book arguing page after page for the existence of God, written by someone who doesn’t believe in God? Or vice versa? Is it a sign of bias, that we never see that?

This isn’t so much a sign of bias, as an effect of a person’s goals. If someone thinks that something is true, he may want others to know that it is true. Normally he would not want others to think that it is false, which would be the expected effect of arguing that it is false.

Nonetheless, the fact that the writer knows where he is going can have bad effects. We saw that in the case of Spinoza’s ethics. But this can happen with anyone: if I am trying to make a point which is in fact false, then I will be likely to make fallacious arguments. Likewise, even if my point is true, but in reality I do not have very good reasons to think it is true, I will be likely to try to make my arguments look stronger than they actually are.

Despite such possibilities, however, the fact that I have a position and that I wish to persuade others gives me some reason to argue for that position rather than arguing for the opposite. Nonetheless, this results from my goal of persuading others. If my goal is to understand the truth myself, arguing one side rather than the other is not helpful: in such a case I should indeed argue both sides, as was done with disputed questions. In other words, the goal of making a point is different from the goal of understanding, and these goals require different means in order to accomplish them.

James Chastek comments on a similar issue:

All the pleas for dialogue I have heard came from the Left, and all of them beggar belief. However sincere the Leftist might be – and I’m not a mind-reader in any position to decide the question – I can’t get beyond the fact that the Leftist himself never follows his own advice by just giving the reasons of his opponents. Why give a speech that “calls for dialogue” when you could give a speech that presents, without comment or judgment, both your own reasons and those of your opponents? Why are calls for dialectic so reliably non-dialectical?

So you want dialogue? Great. You first. Explain the arguments of the other side without continually relating to them as things to be refuted. I can’t do this, even after many years of criticizing my own thoughts and trying to find real insights in opponents (each of whom are sure believe, with some justification, that my thoughts are far more narrow than they seem to me.)

The goal of making your point only requires that you be able to make arguments for your position, but the goal of understanding requires that you be able to make the opposing arguments as well. So if you can’t do this, there is likely a great deal lacking to your understanding of reality.

In the following posts, for illustration, I will argue both sides of various positions.

Making Arguments vs. Manipulating Symbols

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There is still another problem with Spinoza’s manner of argumentation. Spinoza is trying to get geometrical certainty about metaphysics by a logical arrangement of his claims. But this cannot work even in principle. If you take the rules of logic and the forms of the syllogisms, and fit sentences into them using their mere verbal patterns, without thinking about what you are saying, what it means and in what sense it is true or untrue, then you are manipulating symbols, not actually making arguments, and it may well mean that your conclusion is false, whether or not each of your premises is true in some way.

Alexander Pruss, in a recent blog post, argues for the existence of God from certain facts about language:

This argument is valid:

  1. All semantic truths are knowable to members of the community of language users.
  2. There are semantic truths that are not knowable to human language users.
  3. Therefore, there is at least one non-human language user.

There is some reason to accept (1) in light of the conventionality of language. Premise (2) is going to be quite controversial. I justify it by means of a standard argument for epistemicism. Consider Queen Elizabeth II. There are 88 statements of the form:

  • Elizabeth was not old at age n but she was old at age n+1

where n ranges from 1 to 88. It’s a straightforward matter of classical logic to show that if all 88 statements are false, then:

  1. Elizabeth was old at age 1 or Elizabeth is not old at age 89.

But (4) is clearly false: Her Majesty is old now at age 89, and she surely wasn’t old at age one. So, at least one of the 88 statements is false. This means that there is a sharp transition from being not old to being old. But it is clear that no matter what we find out about our behavior, biology and other relevant things, we can’t know exactly where that transition lies. It seems very plausible that the relevant unknowable fact about the transition is a semantic fact. Hence, (2) is true.

The most plausible candidate for the non-human language user who is capable of knowing such semantic facts is God. God could institute the fundamental semantic facts of human language and thereby know them.

(“So, at least one of the 88 statements is false” should be “So, at least one of the 88 statements is true.”) I would consider this to be more a case of manipulating symbols than of making a serious argument.

An atheist is likely to say about this argument, “Wait a minute. Maybe it’s not obvious to me what is wrong with your argument. But there’s just no way you can prove the existence of God from simple facts about how words are used. So there must be something wrong with the argument.”

I agree with the hypothetical atheist that reasonable intuitions would say that you cannot prove the existence of God in such a way, and that this is a reason for doubting the argument even if you cannot formally point out what is wrong with it.

But in fact I think there are two basic problems with it. In the first place, Pruss seems to be failing to consider the actual meaning of his premises. He says, “There is some reason to accept (1) in light of the conventionality of language.” What does this mean? A semantic fact is a fact about the meaning of words or sentences. Pruss is arguing that all facts about the meanings of words or sentences should be knowable to members of the community of language users, and that we should accept this because language is conventional. In other words, human beings make up the meanings of words and sentences. So they can know these meanings; whatever they cannot know about the meaning is not a part of the meaning, since they have not invented it.

But later Pruss says:

This means that there is a sharp transition from being not old to being old. But it is clear that no matter what we find out about our behavior, biology and other relevant things, we can’t know exactly where that transition lies. It seems very plausible that the relevant unknowable fact about the transition is a semantic fact. Hence, (2) is true.

But if this is right, it undercuts the justification for believing the first premise. For the only reason we had to believe that all of the semantic facts are knowable to the community of language users, was a reason to believe that they were knowable to human beings. If they are not knowable to human beings, we no longer have a reason to believe that they are knowable to anyone, or at any rate not a reason that Pruss has given.

This illustrates my point about the necessity of considering the meaning of what you are saying. The argument for the first premise is in fact an argument that human beings can know all of the semantic facts; thus if they cannot, we no longer have a good reason to accept the first premise. We cannot simply say, “This argument is logically valid, we’ve given a reason for the first and a reason for the second, that gives us reason to accept the conclusion.” We need to think about what those reasons are and how they fit together.

The second problem with this argument is that the “standard argument for epistemicism” is just wrong. And likewise, the argument consists of precisely nothing but manipulating words, without thinking about the meaning behind them. It is a “a straightforward matter of classical logic” in the sense that we can fit these words into the logical forms, but this does not mean that this process is telling us anything about reality.

To see this, consider this new word that we can construct by convention, namely “zold.” A person who is between 80 and 90 years old is said to be zold; a person who is between 1 and 10 years old is said not to be zold.

Now consider the 88 statements of the form, “Elizabeth was not zold at age n but she was zold at age n+1.” It’s a straightforward matter of classical logic to show that if all 88 statements are false, then either Elizabeth was zold at age 1, or she was not zold at age 89. But this is clearly false according to the conventions already defined. So at least one of the statements must be true, and there is a sharp transition from being not zold to being zold. It is obvious that no matter what we find out about human beings, that will not tell us where the transition is; the transition must be a semantic fact, a fact about the meaning of the word “zold.”

Obviously, in reality there is no such semantic fact. The convention that we used to define the word simply does not suffice to generate a sharp transition. The problem with the argument for the sharp transition is that the rules of logic presuppose perfectly well defined terms, and this term is not perfectly well defined.

And it is not difficult to see that the word “old” does not differ in a meaningful way from the word “zold.” In reality the two come to have meaning in very similar ways, and in a such a way that there cannot be a sharply defined transition, nor can classical logic force there to be such a sharp transition.

It is not enough to fit your sentences into a logical form. If you want the truth, the hard work of thinking about reality cannot be avoided.

Spinoza’s Geometrical Ethics

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Benedict Spinoza, admiring the certainty of geometry, writes his Ethics Demonstrated in Geometrical Order in a manner imitating that of Euclid’s Elements.

Omitting his definitions and axioms for the moment, we can look at his proofs. Thus we have the first:

1: A substance is prior in nature to its states. This is evident from D3 and D5.

The two definitions are of “substance” and “mode,” which latter he equates with “state of a substance.” However, neither definition explains “prior in nature,” nor is this found in any of the other definitions and axioms.

Thus his argument does not follow. But we can grant that the claim is fairly reasonable in any case, and would follow according to many reasonable definitions of “prior in nature,” and according to reasonable axioms.

He proceeds to his second proof:

2: Two substances having different attributes have nothing in common with one another. This is also evident from D3. For each ·substance· must be in itself and be conceived through itself, which is to say that the concept of the one doesn’t involve the concept of the other.

D3 and D4 (which must be used here although he does not cite it explicitly in the proof) say:

D3: By ‘substance’ I understand: what is in itself and is conceived through itself, i.e. that whose concept doesn’t have to be formed out of the concept of something else. D4: By ‘attribute’ I understand: what the intellect perceives of a substance as constituting its essence.

Thus when he speaks of “substances having different attributes,” he means ones which are intellectually perceived as being different in their essence.

Once again, however, “have nothing in common” is not found in his definitions. However, it occurs once in his axioms, namely in A5:

A5: If two things have nothing in common, they can’t be understood through one another—that is, the concept of one doesn’t involve the concept of the other.

The axiom is pretty reasonable, at least taken in a certain way. If there is no idea common to the ideas of two things, the idea of one won’t be included in the idea of the other. But Spinoza is attempting to draw the conclusion that “if two substances have different attributes, i.e. are different in essence, then they have nothing in common.” But this does not seem to follow from a reasonable understanding of D3 and D4, nor from the definitions together with the axioms. “Dog” and “cat” might be substances, and the idea of dog does not include that of cat, nor cat the idea of dog, but they have “animal” in common. So his conclusion is not evident from the definition, nor does it follow logically from his definitions and axioms, nor does it seem to be true.

And this is only the second supposed proof out of 36 in part 1 of his book.

I would suggest that there are at least two problems with his whole project. First, Spinoza knows where he wants to get, and it is not somewhere good. Among other things, he is aiming for proposition 14:

14: God is the only substance that can exist or be conceived.

This is closely related to proposition 2, since if it is true that two different things can have nothing in common, then it is impossible for more than one thing to exist, since otherwise existence would be something in common to various things.

Proposition 14 is absolutely false taken in any reasonable way. Consequently, since Spinoza is absolutely determined to arrive at a false proposition, he will necessarily employ falsehoods or logical mistakes along the way.

There is a second problem with his project. Geometry speaks about a very limited portion of reality. For this reason it is possible to come to most of its conclusions using a limited variety of definitions and axioms. But ethics and metaphysics, the latter of which is the actual topic of his first book, are much wider in scope. Consequently, if you want to say much that is relevant about them, it is impossible in principle to proceed from a small number of axioms and definitions. A small number of axioms and definitions will necessarily include only a small number of terms, and speaking about ethics and metaphysics requires a large number of terms. For example, suppose I wanted to prove everything on this blog using the method of definitions and axioms. Since I have probably used thousands of terms, hundreds or thousands of definitions and axioms would be required. There would simply be no other way to get the desired conclusions. In a similar way, we saw even in the first few proofs that Spinoza has a similar problem; he wants to speak about a very broad subject, but he wants to start with just a few definitions and axioms.

And if you do employ hundreds of axioms, of course, there is very little chance that anyone is going to grant all of them. They will at least argue that some of them might be mistaken, and thus your proofs will lose the complete certainty that you were looking for from the geometrical method.

 

Everything Proves It

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G. K. Chesterton, in his book Orthodoxy, discusses the meaning of being “entirely convinced” of something:

It is very hard for a man to defend anything of which he is entirely convinced. It is comparatively easy when he is only partially convinced. He is partially convinced because he has found this or that proof of the thing, and he can expound it. But a man is not really convinced of a philosophic theory when he finds that something proves it. He is only really convinced when he finds that everything proves it. And the more converging reasons he finds pointing to this conviction, the more bewildered he is if asked suddenly to sum them up. Thus, if one asked an ordinary intelligent man, on the spur of the moment, “Why do you prefer civilisation to savagery?” he would look wildly round at object after object, and would only be able to answer vaguely, “Why, there is that bookcase … and the coals in the coal-scuttle … and pianos … and policemen.” The whole case for civilisation is that the case for it is complex. It has done so many things. But that very multiplicity of proof which ought to make reply overwhelming makes reply impossible.

We could think about this in terms of probability. The person who is “entirely convinced” would be like the person who assigns a probability of 100%, while someone who is “partially convinced” might assign a somewhat lower probability.

As Chesterton says, the person who assigns the lower probability has no difficulty defending his position. He can point to various things which he has found, arguments and evidence, that support his position.

But what about the person who assigns the probability of 100%? According to Chesterton, he is in difficulty because he finds that everything supports his position. And indeed, this is reasonable. For if some things support your position and some things do not, how could you suppose that there is no chance that you are mistaken? On the other hand, if you think that literally everything supports your position, you might well suppose that you cannot be mistaken about it.

Of course, as we have said many times on this blog, it is unreasonable in fact to claim such certainty, and it is unreasonable in fact to claim that everything supports your position. So being “entirely convinced” in Chesterton’s sense here is a bad thing, not a good thing.

Chesterton goes on to apply this to his belief in Catholicism:

There is, therefore, about all complete conviction a kind of huge helplessness. The belief is so big that it takes a long time to get it into action. And this hesitation chiefly arises, oddly enough, from an indifference about where one should begin. All roads lead to Rome; which is one reason why many people never get there. In the case of this defence of the Christian conviction I confess that I would as soon begin the argument with one thing as another; I would begin it with a turnip or a taximeter cab.

This is not a good thing, for the above reasons. We could describe this situation in another way. We saw in the previous post that consistent testimony where there should be inconsistent testimony leads to a weakening of the evidence. If a dozen eyewitnesses agree in every respect, this is not good evidence for their claim, but good evidence that they are collaborating. In a similar way, if it seems to you that “everything proves it,” this is very good evidence that you are incapable of distinguishing between things that support your position and things that do not.

This also provides a fuller explanation for the fact that the person who is entirely convinced in Chesterton’s sense finds it difficult to argue for his position. Chesterton’s point that when there are too many possibilities, it is difficult to choose one of them, has some validity. But more fundamentally, the person who is entirely convinced in this way is not even engaging in reasonable argument in the first place; while the person who is partially convinced at least has the possibility of engaging in this kind of argument.

Too Much Evidence

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Lachlan J. Gunn et alia argue in a paper, “Too good to be true: when overwhelming evidence fails to convince,” that in some situations, as you apparently gather evidence in favor of a theory, it becomes less and less likely to be true:

In this paper, for the first time, we perform a Bayesian mathematical analysis to explore the question of multiple confirmatory measurements or observations for showing when they can—surprisingly—disimprove confidence in the final outcome. We choose the striking example that increasing confirmatory identifications in a police line-up or identity parade can, under certain conditions, reduce our confidence that a perpetrator has been correctly identified.

Imagine that as a court case drags on, witness after witness is called. Let us suppose thirteen witnesses have testified to having seen the defendant commit the crime. Witnesses may be notoriously unreliable, but the sheer magnitude of the testimony is apparently overwhelming. Anyone can make a misidentification but intuition tells us that, with each additional witness in agreement, the chance of them all being incorrect will approach zero. Thus one might naïvely believe that the weight of as many as thirteen unanimous confirmations leaves us beyond reasonable doubt.

However, this is not necessarily the case and more confirmations can surprisingly disimprove our confidence that the defendant has been correctly identified as the perpetrator. This type of possibility was recognised intuitively in ancient times. Under ancient Jewish law, one could not be unanimously convicted of a capital crime—it was held that the absence of even one dissenting opinion among the judges indicated that there must remain some form of undiscovered exculpatory evidence.

This is an interesting situation, and someone might suppose that it is one where the evidence changes sides.

But this does not follow. The reality is a bit different. Suppose you flip a coin thirty times, and get heads every time. Each time you get heads, you receive evidence in favor of the hypothesis, “I am having a really lucky streak.” But each time you also receive evidence, and stronger evidence, in favor of the hypothesis, “This coin is biased.” After flipping it thirty times, you thus are likely to become very convinced of the latter hypothesis, and thus convinced that the former is mistaken. But this did not happen because at some point the evidence went from one side to the other, but because the evidence supported two different theories, and one more than the other.

However, regardless of exactly how we describe the situation here, this does have important consequences for the evaluation of multiple instances of testing the same thing. In the case of the police line-up discussed in the article, we know from experience that people are far from infallible in their identification. So if you have a large number of people who identify the same person, without any exception, that is strong evidence that the process is biased; perhaps the police encouraged the people to identify a particular person, for example. Likewise, eyewitness testimony tends not to be perfectly accurate. Consequently, if we take the testimony of many eyewitnesses to the same complex events, and there is not the slightest discrepancy, this is good evidence that their testimony is biased. Perhaps someone created a story and instructed them not to deviate from it, for example. And on the other hand, minor discrepancies in such accounts do not weaken their testimony, but strengthen it (although not to the discrepant point itself), by making it less likely that they are biased in such a way.

 

Predicting the Future

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Despite the opinion of David Hume, we find it possible to predict many things about the future. I will have breakfast tomorrow. Some people will celebrate New Year’s Day on January 1st, 2016. The Jehovah’s Witnesses will continue to modify their predictions for the end of the world.

Despite this ability to say a few things about the future, however, if our predictions are sufficiently detailed they are guaranteed to fail. In part this is true simply because our knowledge is not good enough, but there is another reason, one which would guarantee that such predictions would fail even if made by someone with perfect knowledge.

Suppose I have perfect knowledge of the future, and I write down in a book everything that I think you will do for the rest of your life, in nearly every detail, saying at what time of day you will perform various actions such as brushing your teeth, and so on. Then I give you the book. For the first few days, you do everything that is written there, in every detail.

At some point you are pretty sure to wonder whether you can do something different from what the book says. It says that you will eat breakfast at 7:10 AM one morning, so you decide to test violating that, and eat at 7:30 instead. Presumably, nothing will force you to eat breakfast earlier than you planned, and so the prediction will be falsified.

The situation here is very much like the Liar Game in the previous post. The statements have a truth value, and are not objectively paradoxical. But the player cannot get them right, because the truth value of the last statement is anti-correlated with his judgment. In the same way, given human beings with the psychological makeup that they actually have, and the physical abilities that they actually have, a detailed prediction of the future which is known to people will be at least in some respects anti-correlated with reality.

In this sense, the impossibility comes up because the predictions are made known to people. The argument does not prove that there could not be a book somewhere with the whole of the future laid out in detail; but such a book cannot be actually discovered by people without failing to predict the future correctly.

 

Liar Game

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While this is the name of a certain story, it is also the name I am giving to the game I am about to propose. The rules are that I propose a certain number of statements, and the player has to categorize them as true or false. The player wins if all of them are correctly categorized, and fails if he does not categorize them all, or if he mistakenly categorizes a true statement as false, or a false statement as true. It is against the rules for him to place a statement in both categories.

The statements I propose are the following:

  1. 2+2=4.
  2. 2+2=5.
  3. The player will categorize this as false.

It can easily be seen that the player is guaranteed to lose the game. If the player does not categorize the third statement, then it is false, and he has failed to categorize them all. On the other hand, if he categorizes it as true, it is false, and if he categorizes it as false, it is true. In any case either he fails to categorize it, or he categorizes it incorrectly.

It is evident that this is related to the paradox of the Liar, but there is a significant difference. The original liar statement is paradoxical, in the sense that applying the ordinary rules of logic results in a contradiction regardless of whether one considers the statement to be true or false.

This is not the case here. There is nothing paradoxical about the statement, in this sense. Given an actual player and an actual instance of playing the game, the statement will plainly be true or false in an objective sense, and without any contradiction being implied. It is just that the player cannot possibly categorize it correctly, since its truth is correlated with the player categorizing it as false.

 

More on Thought and Language

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In the previous post we were considering the relationship of thought and language. There are other ways to notice the close connection. From time to time I have the experience (which I think is not uncommon for others as well) of thinking something, or perhaps being about to think something, but then being distracted before being able to internally verbalize the thought. Afterwards there is no easy way to recover the thought without going through the chain of imagination and thought that led up to that point. And if this is not done at the time, it may be impossible to ever recover the thought. This is perhaps most directly because memory depends on the imagination, and consequently we do not remember our thoughts without either some associated verbalization or the equivalent.

This can have various consequences. For one thing, thinking a thought is rather like speaking to oneself, and needs interpretation just as we need to interpret the speech of others. You might assume that you automatically understand yourself, since you are the one thinking the thought, but this is not necessarily the case. Each time you remember a thought, you are doing it through a verbalization, which is itself a vague expression which could be understood in more than one way. This implies that you may not even be thinking exactly the same thought each time.

This influences the way we learn or change our minds. Thus for example Thomas Talbott criticizes John Loftus’s book The Outsider Test for Faith:

By way of a partial answer to such questions, Loftus suggests that most religious people, even among the most intelligent and reflective, never (formally) convert to another religion or de-convert from their initially acquired religion viewed as a cultural phenomenon: “In most cases,” he says, “we rarely stray from what we were raised in but merely move around among versions of the same general religion…” (p. 83). My own informal impression, however, is that, depending upon how one might measure such things, many people travel a huge distance (in a host of different directions) over the course of a normal lifespan; and many observers, such as hospice workers who work with end of life issues, sometimes report great spiritual growth, as they interpret it, in the final days and weeks of a person’s earthly life. Beyond that, I see no reason to deny that even very small movements, as judged from the outside, can sometimes signify profound spiritual progress. Do I rest any argument of substance on such subjective matters, or expect to achieve universal agreement on them? Not at all. But I do suggest that one should not trivialize, as Loftus appears to do above, what it might mean to “move around among versions of the same general religion.”

Here is why. The Christian tradition, which is the religious tradition I know best, is so rich and includes so much diversity within it that the question of diversity between the Christian tradition as a whole and some other religious tradition, such as Islam, may have little or no coherent meaning. Put it this way: A cultural Christian has no need to embrace another religious or cultural tradition, at least not formally, in order to embrace religious views typically associated with some other tradition. Take, for example, the great Christian poet John Milton, who emphatically rejected the one substance theory of the Trinity, adopted the Arian view that Jesus Christ was on a lower ontological level than God the Father, and even set forth an elaborate biblical argument in defense of polygamy. He had no need, in other words, to embrace the Muslim religion as a cultural phenomenon in order to embrace a concept of God that was virtually identical with the Muslim concept; yet, C. S. Lewis and others (including myself) still consider him a great Christian poet. Similarly, those Christians who come to believe in reincarnation, as more than a few do despite their upbringing, have no need to embrace all the nuances of the typical Hindu understanding and certainly have no need to embrace all of the cultural trappings and conventions of some particular sect in the Hindu religion. My point is that moving “around among versions of the same general religion” may involve profound (and easy to overlook) changes in one’s religious outlook, changes that may be at least as momentous as converting to another religion (or even as adopting a kind of practical atheism). For as Loftus himself points out, “Worldviews are dynamic rather than static things, anyway. They are constantly changing with additional education and experience” (p. 97). So again I ask: Given such dynamism and so many dynamic opportunities for spiritual growth (however that should be construed) within any one of the great religious traditions, why should it even matter where one’s spiritual journey begins?

There are several reasons why things work this way. In the first place, belonging to a religion does not in itself signify a certain belief, but membership in a religious community. This implies that changing your mind about religious matters does not necessarily imply changing your religion, and it may be more reasonable not to change it, depending on various circumstances. But there is another reason. Due to the vice of pride and various other causes, we do not like to say, “I was wrong.”

Not only in religion but in almost every other matter, changes of opinion are significantly more frequent than the actual admission of having been wrong about something. One can avoid admitting this in various ways, some deliberate, some usually subconscious. Sometimes a person will say nothing for a while, then begin to voice the new opinion, hoping that no one notices that he has changed his mind, since this would be to admit that he was wrong. Occasionally a person may even assert that he always held the new opinion, and he may even believe this, perhaps since he now finds it difficult to imagine holding another position, and consequently difficult to remember doing so, since memory depends on the imagination. Or a person may wait until he leaves one social circle and joins another, before starting to say something new, so that no one notices the change of mind. Or again, one can voice the new opinion using the same words that were used to express the old opinion. In this case one may or may not even notice that one has changed one’s mind. Or one can change one’s mind gradually, in such a way that at each stage the same words are used, and it is actually reasonable to call it the same opinion, perhaps with a variation of degree or emphasis. But at the end it may no longer be reasonable to call it the same opinion, just as a color may be changed by imperceptible stages until a new color is present. The person himself, however, may still not recognize that he has ever changed his opinion at all.

The vagueness discussed in the previous post is closely related to all of this. The boundaries of a word are vague; thus there is a region where it is vague whether a person is bald or not. And likewise the boundaries of the vague region are themselves vague; at no level will complete precision be found. This makes it all the easier for an opinion to drift gradually and in an almost unnoticeable way over time.